Intervention analysis with missing data

Abstract

Intervention analysis is a potentially useful tool for modeling time series when the process mean undergoes changes as the result of an external perturbation. The utility of the technique for water resource applications is, however, limited by the requirement that the data be collected uniformly in time. Two approaches for estimating missing data, one of which provides minimum variance estimates when model parameters are known, and a computationally simpler approximation were investigated. The approximation was found to be quite adequate and was incorporated in a practical scheme to estimate missing data and model parameters simultaneously. Subsequently, a method for estimating the parameter variance for use in significance tests on the intervention magnitude was investigated. The adequacy of the approximation was assessed in a series of Monte Carlo tests using three models consisting of step, linear, and impulse decay trends in mean with residual lag 1 Markov noise. Results of the experiments indicated that the suggested method provides adequate estimates of the variance of the intervention magnitude of the step and impulse decay models but that the variance was substantially overestimated for the linear model. However, for the same proportion of missing data the accuracy of the approximation improved as the sample size increased.